Rumors in a network: Who's the culprit?

IEEE Transactions on Information Theory

Volumn 57, Issue 8, 2011, Pages 5163-5181

  Shah, Devavrat ^a   Zaman, Tauhid ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Complex networks; detection algorithms; graph theory; inference algorithms; maximum likelihood (ML) detection; probability

Indexed keywords

COMMON NETWORKS; COMPLEX NETWORKS; DETECTION ALGORITHMS; DETECTION PROBABILITIES; ELECTRIC POWER GRIDS; GENERAL NETWORKS; INFERENCE ALGORITHM; MAXIMUM LIKELIHOOD (ML) DETECTION; MAXIMUM LIKELIHOOD ESTIMATOR; NETWORK TOPOLOGY; REAL NETWORKS; RUMOR SPREADING; SCALE FREE NETWORKS; SMALL WORLDS; SYNTHETIC NETWORKS; SYSTEMATIC STUDY; THRESHOLD PHENOMENA;

ALGORITHMS; ELECTRIC NETWORK TOPOLOGY; ESTIMATION; GRAPH THEORY; INFERENCE ENGINES; MAXIMUM LIKELIHOOD; PLANT EXTRACTS; PROBABILITY;

COMPUTER SIMULATION;

EID: 79961005336     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2158885     Document Type: Article

References (27)

1. N. T. J. Bailey, The Mathematical Theory of Infectious Diseases and its Applications. London, U.K.: Griffin, 1975.
2. C. Moore and M. E. J. Newman, "Epidemics and percolation in in small-world networks," Phys. Rev. E, vol. 61, pp. 5678-5682, 2000.
3. R. Pastor-Satorras and A. Vespignani, "Epidemic spreading in scalefree networks," Phys. Rev. Lett., vol. 86, pp. 3200-3203, 2001.
4. M. E. J. Newman, "The spread of epidemic disease on networks," Phys. Rev. E, vol. 66, p. 016128, 2002.
5. A. Ganesh, L. Massoulie, and D. Towsley, "The effect of network topology on the spread of epidemics," in Proc. 24th Ann. Joint Conf. IEEE Comput. Commun. Soc. (INFOCOM), 2005, vol. 2, pp. 1455-1466. (Pubitemid 41390795)
6. N. Demiris and P. D. O'Neill, "Bayesian inference for epidemics with two levels of mixing," Scand. J. Statist., vol. 32, pp. 265-280, 2005. (Pubitemid 40747186)
7. G. Streftaris and G. J. Gibson, "Statistical inference for stochastic epidemic models," in Proc. 17th Int. Workshop on Statist. Model., 2002, pp. 609-616.
8. P. D. O'Neill, "A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods," Math. Biosci., vol. 180, pp. 103-114, 2002. (Pubitemid 35304348)
9. N. Demiris and P. D. O'Neill, "Bayesian inference for stochastic multitype epidemics in structured populations via random graphs," J. Roy. Statist. Soc. B, vol. 67, pp. 731-745, 2005. (Pubitemid 41692387)
10. H. Okamura, K. Tateishi, and T. Doshi, "Statistical inference of computer virus propagation using nonhomogeneous poisson processes," in Proc. 18th IEEE Int. Symp. Software Reliabil., 2007, vol. 5, pp. 149-158.
11. W. Evans, C. Kenyon, Y. Peres, and L. Schulman, "Broadcasting on trees and the Ising model," Ann. Appl. Prob., vol. 10, pp. 410-433, 2000.
12. E. Mossel, "Reconstruction on trees: beating the second eigenvalue," Ann. Appl. Prob., vol. 11, pp. 285-300, 2001.
13. A. Gerschenfeld and A. Montanari, "Reconstruction for models on random graphs," in Proc. 48th IEEE Symp. Found. Comp. Sci., 2007, pp. 194-204.
14. G. Sabidussi, "The centrality index of a graph," Psychometrika, vol. 31, pp. 581-603, 1966.
15. L. C. Freeman, "A set of measure of centrality based on betweenness," Sociometry, vol. 40, pp. 35-41, 1977.
16. J. M. Hammersley and D. J. A. Welsh, "First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory," in Bernoulli-Bayes-Laplace Anniversary Volume. Berlin: Springer, 1965.
17. R. Smythe and J. C.Wierman, First Passage Percolation on the Square Lattice, Lecture Notes in Math. Berlin: Springer, 1978.
18. J. T. Cox and R. Durrett, "Some limit theorems for percolation processes with necessary and sufficient conditions," Ann. Appl. Prob., vol. 9, pp. 583-603, 1981.
19. H. Kesten, Aspects of First Passage Percolation. Lecture Notes in Math. Berlin: Springer, 1986, vol. 1180, pp. 125-264.
20. H. Kesten, "Percolation theory and first-passage percolation," Ann. Appl. Prob., vol. 15, pp. 1231-1271, 1987.
21. H. Kesten, "On the speed of convergence in first-passage percolation," Ann. Appl. Prob., vol. 3, pp. 296-338, 1993.
22. M. D. Atkinson, "On computing the number of linear extensions of a tree," Order, vol. 7, pp. 23-25, 1990.
23. G. Brightwell and P. Winkler, "Counting linear extensions is #P-complete," in JSTOC '91: Proc. 23rd Ann. ACM Symp. Theory of Comput., 1991, pp. 175-181.
24. D. J.Watts and S. Strogatz, "Collective dynamics of 'small-world' networks," Nature, vol. 393, pp. 440-442, 1998. (Pubitemid 28292183)
25. A. Barabasi and R. Albert, "Emergence of scaling in random networks," Science, vol. 286, pp. 509-512, 1999.
26. The CAIDA AS relationships dataset Aug. 30, 2009 [Online]. Available: http://www.caida.org/data/active/as-relationships/
27. D. Betsekas and J. N. Tsitsiklis, Probabilistic System Analysis, 2nd ed. New York: Aetna, 2009.